math119: begin multivariable functions

docs/1b/math119.md

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 ## Multivariable functions
 
+!!! definition
+    - A **multivariable function** accepts more than one independent variable, e.g., $f(x, y)$.
+
+The signature of multivariable functions is indicated in the form *[identifier]*: *[input type]* → *[return type]*. Where $n$ is the number of inputs:
+
+$$f: \mathbb R^n \to \mathbb R$$
+
+!!! example
+    The following function is in the form $f: \mathbb R^2\to\mathbb R$ and maps two variables into one called $z$ via function $f$.
+    
+    $$(x,y)\longmapsto z=f(x,y)$$
+
 ### Sketching multivariable functions
+
+!!! definition
+    - In a **scalar field**, each point in space is assigned a number. For example, topography or altitude maps are scalar fields.
+    - A **level curve** is a slice of a three-dimensional graph by setting to a general variable $f(x, y)=k$. It is effectively a series of contour plots set in a three-dimensional plane.
+    - A **contour plot** is a graph obtained by substituting a constant for $k$ in a level curve.
+
+Please see [level set](https://en.wikipedia.org/wiki/Level_set) and [contour line](https://en.wikipedia.org/wiki/Contour_line) for example images.f
+